The highly infectious SARS-CoV-2 novel coronavirus has resulted in a global pandemic. More than a hundred million people are already impacted, with infected numbers expected to go up. Coughing, sneezing, and even talking emit respiratory droplets which can carry infectious viruses. It is important to understand how the exhaled particles move through air to an exposed person to better predict the airborne transmission impacts of SARS-CoV-2. There are many studies conducted on the airborne spread of viruses causing diseases such as SARS and measles; however, there are very limited studies that couple the transport characteristics with the aerosol dynamics of the droplets. In this study, a comprehensive model for simultaneous droplet evaporation and transport due to diffusion, convection, and gravitational settling is developed to determine the near spatial and temporal concentration of the viable virus exhaled by the infected individual. The exposure to the viable virus is estimated by calculating the respiratory deposition, and the risk of infection is determined using a dose-response model. The developed model is used to quantify the risk of short-range airborne transmission of SARS-CoV-2 from inhalation of virus-laden droplets when an infected individual is directly in front of the person exposed and the surrounding air is stagnant. The effect of different parameters, such as viral load, infectivity factor, emission sources, physical separation, exposure time, ambient air velocity, dilution, and mask usage, is determined on the risk of exposure.